Convergence of weighted sums of random functions in D[0, 1]

Peter Z. Daffer

Journal of Multivariate Analysis, 1991, vol. 38, issue 2, 319-332

Abstract: Conditions are investigated which imply the tightness of certain weighted sums [Sigma]i = 1kn aniXi of random functions (Xn) taking values in D([0, 1]; E), where E is a separable Banach space. Improved weak laws of large numbers result as corollaries. Examples are presented to clarify the relative strengths of the moment conditions and their relationship to tightness and the strong law of large numbers. A tightness condition is defined using a certain class of sets measurable in the Skorokhod J1-topology, which yields J1-tightness of sequences of weighted sums. As a consequence, tightness of a sequence (Xn) in the Skorokhod M1-topology is used to obtain J1-tightness of a sequence () of averages and a strong law of large numbers in D(R+).

Keywords: weighted; sums; tightness; moment; conditions; Skorokhod; topologies; laws; of; large; numbers (search for similar items in EconPapers)
Date: 1991
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(91)90049-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:38:y:1991:i:2:p:319-332

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().